# nLab Sandbox

What is the class in $\pi_4(S^3) \simeq \mathbb{Z}_2$ of the map

$\array{ S^{\mathbb{H}} &\longrightarrow& S^{\left(\mathbb{H}_{im}\right)} \\ q &\mapsto& q v \bar q }$

where $v \in \mathbb{H}_{im} \setminus \{0\}$ is any non-zero imaginary quaternion?

An XY-Matrix diagram:

\begin{tikzpicture}

\draw (0,0) -- (2,0) -- (2,-2);

\end{tikzpicture}

cellular model

Last revised on February 16, 2019 at 10:19:40. See the history of this page for a list of all contributions to it.